On the l^{q,p} cohomology of Carnot groups

Pierre Pansu (1) , Michel Rumin (1)

1 LMO - Laboratoire de Mathématiques d'Orsay

We study the simplicial ℓ q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.

Mots clés: Riesz operator; geometric group theory; global analysis; Heisenberg group; $\ell^{q; p}$ cohomology; Carnot group

Domaines: Analyse fonctionnelle [math.FA]; Géométrie différentielle [math.DG]

Pierre Pansu, Michel Rumin. On the l^{q,p} cohomology of Carnot groups. Annales Henri Lebesgue, 2018, 1, p. 267-295. ⟨10.5802/ahl.8⟩. ⟨hal-01713354⟩